Upper and lower variational estimates in calculating the three-particle systems with exponential trial functions

All the formulas necessary for calculating not only the upper $E_U$, but also the lower $E_L$ variational estimates of three-particle system energy with the use of trial functions in the form of expansions in multi-dimensional exponents are obtained. The lower variational estimates with such trial functions are found for the first time. It is shown on some examples that, though $E_L$ is usually a more distant estimate of the system energy exact value $E_0$ than $E_U$, it provides also an appreciably more reliable extrapolation.